Yes, you need "be" in "He is thought to be a wealthy man", in the same way as you need the present of "be" in "He is a wealthy man"- "He a wealthy man" is obviously wrong.

I don't think it's very useful to tell students that this is the passive, as it has little in common with "Wine is grown in Southern France" and "The television was invented by Baird". It's less confusing just to teach it with other similar forms like "He is said to..." and even "Apparently..."